Statistical properties of the gravitational force through ordering statistics

Overview & Synopsis

We study the statistical distribution of Newtonian gravitational forces acting on a test particle embedded in an infinite, homogeneous, and uncorrelated random gas of particles. In the limit where both the number of neighboring particles and the confining volume tend to infinity with constant density, this distribution converges to the classic Holtsmark distribution. Our focus here is on the contribution of the nearest particle neighbors to the total Newtonian force. To this end, we derive the joint spatial distribution of the nearest neighbors in arbitrary spatial dimensions, and show that, in three dimensions, the divergence of the Holtsmark distribution's variance originates entirely from the dominant influence of the nearest neighbor.